| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.48 |
| Score | 0% | 50% |
A machine in a factory has an error rate of 4 parts per 100. The machine normally runs 24 hours a day and produces 9 parts per hour. Yesterday the machine was shut down for 9 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 129.6 | |
| 114 | |
| 185.2 | |
| 86.4 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{4}{100} \) x 9 = \( \frac{4 \times 9}{100} \) = \( \frac{36}{100} \) = 0.36 errors per hour
So, in an average hour, the machine will produce 9 - 0.36 = 8.64 error free parts.
The machine ran for 24 - 9 = 15 hours yesterday so you would expect that 15 x 8.64 = 129.6 error free parts were produced yesterday.
What is \( 4 \)\( \sqrt{125} \) - \( 4 \)\( \sqrt{5} \)
| 16\( \sqrt{25} \) | |
| 0\( \sqrt{125} \) | |
| 16\( \sqrt{5} \) | |
| 0\( \sqrt{0} \) |
To subtract these radicals together their radicands must be the same:
4\( \sqrt{125} \) - 4\( \sqrt{5} \)
4\( \sqrt{25 \times 5} \) - 4\( \sqrt{5} \)
4\( \sqrt{5^2 \times 5} \) - 4\( \sqrt{5} \)
(4)(5)\( \sqrt{5} \) - 4\( \sqrt{5} \)
20\( \sqrt{5} \) - 4\( \sqrt{5} \)
Now that the radicands are identical, you can subtract them:
20\( \sqrt{5} \) - 4\( \sqrt{5} \)On average, the center for a basketball team hits 35% of his shots while a guard on the same team hits 45% of his shots. If the guard takes 30 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?
| 30 | |
| 41 | |
| 31 | |
| 37 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{45}{100} \) = \( \frac{45 x 30}{100} \) = \( \frac{1350}{100} \) = 13 shots
The center makes 35% of his shots so he'll have to take:
shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)
to make as many shots as the guard. Plugging in values for the center gives us:
center shots taken = \( \frac{13}{\frac{35}{100}} \) = 13 x \( \frac{100}{35} \) = \( \frac{13 x 100}{35} \) = \( \frac{1300}{35} \) = 37 shots
to make the same number of shots as the guard and thus score the same number of points.
In a class of 19 students, 9 are taking German and 7 are taking Spanish. Of the students studying German or Spanish, 3 are taking both courses. How many students are not enrolled in either course?
| 16 | |
| 17 | |
| 18 | |
| 6 |
The number of students taking German or Spanish is 9 + 7 = 16. Of that group of 16, 3 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 16 - 3 = 13 who are taking at least one language. 19 - 13 = 6 students who are not taking either language.
If all of a roofing company's 10 workers are required to staff 5 roofing crews, how many workers need to be added during the busy season in order to send 10 complete crews out on jobs?
| 1 | |
| 9 | |
| 10 | |
| 17 |
In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 10 workers at the company now and that's enough to staff 5 crews so there are \( \frac{10}{5} \) = 2 workers on a crew. 10 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 10 x 2 = 20 total workers to staff the crews during the busy season. The company already employs 10 workers so they need to add 20 - 10 = 10 new staff for the busy season.